The Royals are currently in the hunt for a new manager after Steve Coppell brought to an end his near six-year reign following the Championship play-off semi-final defeat to Burnley on Tuesday.
Rodgers, who took over at Vicarage Road in November, has emerged as the bookmakers' favourite to succeed Coppell, but has stressed he is committed to Watford.
He said in the Watford Observer: "For me, in this moment, my full concentration is on next season with Watford.
"There is always going to be speculation as a manager and a coach. You are always honoured if you are linked with big jobs because it means you and your team are doing well.
"But in this moment, my concentration is fully on Watford and looking forward to next year.
"At the moment I am trying to concentrate on my learning at various different clubs and that is what is on my mind at the moment and looking forward to the future with Watford.
"Due to the amount of phone calls I have been having and the speculation, I felt I had to make a comment on it but I am not thinking about it [the Reading job]."
He told the Evening Post: "It's an honour to be even linked with a big club and a terrific job. However, for me nothing has changed.
"I am still manager of Watford which is a terrific club with great supporters, who seem to have accepted me.
"So until I am told otherwise I will just get on with preparing Watford for next season."